Praise be to Allah.
There is no difference between reading Qur’aan from the Mushaf or reading from an electronic Mushaf, or from pages on the Internet, or from the screen of a mobile phone. What counts is reading, moving the lips and looking at the written words of Allah, may He be exalted, and all of that is achieved when reading from an electronic screen. So it attains the reward of reading concerning which the Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever reads a letter of the Book of Allah will have one hasanah (good deed) for it, and the hasanah (good deed) brings a tenfold reward. I do not say that ‘Alif-Laam-Meem’ is a letter; rather Alif is a letter, Laam is a letter and Meem is a letter.”
Narrated by at-Tirmidhi, 2910. classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
It says in al-Mu‘jam al-Waseet (2/360): Reading the Book means following the words with the eyes and uttering them. End quote.
Shaykh al-Islam Ibn Taymiyah said in al-Fataawa al-Kubra, 2/419:
If he reads the Qur’aan for the sake of Allah, may He be exalted, then he will be rewarded for that in all cases. End quote.
With regard to the question of whether wudoo’ is required for this reading, being in a state of purity is not essential for reading Qur’aan, rather it is only essential for touching the Mushaf, because the Prophet (blessings and peace of Allah be upon him) said: “No one should touch the Qur’aan except one who is in a state of purity.”
Narrated in the Muwatta’ of Maalik, 468; classed as saheeh by al-Albaani in Irwa’ al-Ghaleel, 122.
If one who had memorised it recites it, or if it is read from the Mushaf without touching, there is nothing wrong with that.
Based on that, there is nothing wrong with reading Qur’aan from the computer screen without wudoo’, because this is not touching the Holy Qur’aan; rather it is like reading from the Mushaf without touching, just like if the Mushaf is open in front of one and one reads from it without touching it.
See also the answer to question no. 106961
And Allah knows best.